The denominator of a fraction is 4 more than the numerator. If both the denominator and the numerator are increased by 1, the resulting fraction equals ½. What is the original fraction?
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Let's solve this problem step by step:
1. Let's assume the numerator of the fraction is x. This means the denominator would be x + 4, because it's 4 more than the numerator.
2. According to the problem, if both the numerator and denominator are increased by 1, the resulting fraction becomes ½. So the new numerator would be (x + 1), and the new denominator would be (x + 4 + 1) = (x + 5).
3. Now we can write the equation based on the given information:
(x + 1) / (x + 5) = ½
4. To solve this equation, we can cross multiply:
2(x + 1) = x + 5
5. Expanding both sides, we get:
2x + 2 = x + 5
6. Move all terms containing x to one side and the constants to the other side:
2x - x = 5 - 2
7. Simplifying, we have:
x = 3
8. Now we know the numerator is 3, and the denominator is 3 + 4 = 7.
Therefore, the original fraction is 3/7.